There are 6 truncations of the 7-orthoplex. Vertices of the truncation 7-orthoplex are located as pairs on the edge of the 7-orthoplex. Vertices of the bitruncated 7-orthoplex are located on the triangular faces of the 7-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 7-orthoplex. The final three truncations are best expressed relative to the 7-cube.
| bgcolor=#e7dcc3 colspan=2 | Truncated 7-orthoplex | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | 3920 | |
| Faces | 2520 | |
| Edges | 924 | |
| Vertices | 168 | |
| Vertex figure | v | |
| Coxeter groups | B7, [3<sup>5</sup>,4] D7, [3<sup>4,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a truncated 7-orthoplex, centered at the origin, are all 168 vertices are sign (4) and coordinate (42) permutations of
(±2,±1,0,0,0,0,0)
There are two Coxeter groups associated with the truncated 7-orthoplex, one with the C7 or [4,3<sup>5</sup>] Coxeter group, and a lower symmetry with the D7 or [3<sup>4,1,1</sup>] Coxeter group.
| bgcolor=#e7dcc3 colspan=2 | Bitruncated 7-orthoplex | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | 2t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 4200 | |
| Vertices | 840 | |
| Vertex figure | v | |
| Coxeter groups | B7, [3<sup>5</sup>,4] D7, [3<sup>4,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a bitruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±1,0,0,0,0)
The tritruncated 7-orthoplex can tessellation space in the quadritruncated 7-cubic honeycomb.
| bgcolor=#e7dcc3 colspan=2 | Tritruncated 7-orthoplex | |
|---|---|---|
| Type | uniform 7-polytope | |
| Schläfli symbol | 3t | |
| Coxeter-Dynkin diagrams | ||
| 6-faces | ||
| 5-faces | ||
| 4-faces | ||
| Cells | ||
| Faces | ||
| Edges | 10080 | |
| Vertices | 2240 | |
| Vertex figure | v | |
| Coxeter groups | B7, [3<sup>5</sup>,4] D7, [3<sup>4,1,1</sup>] | |
| Properties | convex |
Cartesian coordinates for the vertices of a tritruncated 7-orthoplex, centered at the origin, are all sign and coordinate permutations of
(±2,±2,±2,±1,0,0,0)